limit was measured by a laboratory vane apparatus. These strengths enable the determination of the liquid limit from one test, that is, from one water content. The established relation between the undrained shear strength and corresponding con­ solidation serves to establish the correlation between the liquid limit and plastic limit. The latter can readily be obtained by knowing the liquid limit and the corresponding vane strength.

Table II). If the water content versus the shear strength of the clay samples corresponding to the range of water contents of

( ±. 0.15 wL) are plotted on a double log scale, a group of

straight lines, each representing one sample are obtained (Fig. 2). Points corresponding to the liquid limit of each soil can be joined by a straight line called the wL line for convenience. This line shows clearly that although the

strength at liquid limit is essentially small, a big relative

(Fig. 3). The straight lines are

difference is to be noticed

nearly parallel for all samples (within the range of water contents adopted) and can be considered to have an average

5.9,

slope of /9 =

where w, = w (rf/rn )0-17.

(log Tf — log Tfl)/(log

—

log

w)

=

24

\

21

\

22

15

16 17

2

l8\4SM /6 /l9 /

Fig. 4 is used to determine the liquid limit in terms of the vane strength at water contents near to the liquid limit by

one test for one water content as illustrated in Fig. 3.

knowing the shear strength rf of a remoulded sample and the water content corresponding to this strength which is repre­ sentedby point (1) in Fig. 3, the liquid limit can be determined, which represents the water content at point (3) as illustrated by dashed path 1-2-3.

From the data by Skempton (1957) and others, it is possible to establish the relationship between the ratio of undrained strength to the corresponding overburden pressure C J P and the plasticity index (Iv) of the soil:

By

(1)

where (Iv) is expressed as a number rather than a ratio. Again from consolidation test data on eight soils (Table

C J P

=

0.11

+ 0.0037

(Ip)

WATER

CONTENT

PERCENT

(LOG-SCALE)

f ig . 2. Relation between moisture content and shearing strength.

1 27

WATER

CONTENT- PERCENT (LOG-SCALE)

f i g . 3. Determination of liquid limit from vane shear strength at a moisture content near the liquid limit.

II) as well as from data by Skempton and from other data on remoulded clays, it is found that the void ratio e corre­ sponding to the plastic limit is reached at pressures ranging between 9 and 11 kg/sq.cm. (Fig. 5). For convenience consider this pressure to be 10 kg/sq.cm. Hence from Fig. 6;

Ae =

Cv (log

10 -

log P0)

Ae/5s =

(C JS s)

(1 -

log P0)

but

Ae/Ss = Iv

therefore

/r

=

(Cv/Ss) (1

-

log P 0)

(2)

where

CL. =

.007 (wL — 10)

using Ss =

2.7.

In equation (2) the value of (/,») is essentially inserted as a fraction. Equations (1) and (2) give the estimated con­ solidation pressures corresponding to the liquid limit and the plasticity index. For convenience the two equations can be solved by trial, making use of the relationship between activity and shear strength at liquid limit (Fig. 7) on which values of Iv are indicated. The irregular sequence of values of Iv in Fig. 7 is a result of the lack of correlation between

between void ratio and overburden pressure for clay sediments as a function of the Alter* berg limits.

of plastic

limit from void ratio and strength at liquid limit.

f i g

.

6.

Determination

ACTIVITY

(LOG-SCALE)

f ig . 7. Relationship between shearing strength and activity.

TABLIC III. M EASU RED VERSUS CALCULATED VALUES OF PLASTIC LIM IT

No.

Locality

1 Qalyuob 2

Cairo

3 Qalyuob

4 Alexandria

5 Tanta

6 Talkha

7 Cairo west

8 Abu Zenema

Liquid

Plastic limit,

limit

standard test

(at P

67

25 .8

69

32

")

70

25

77

36

8

86

25

80

39 .2

72

27

33

20 . 5

Plastic limit = 10 kg/sq. cm.)

Plastic* limit calculated from eqn. (1) and (2)

27

35.5

28.5

36.5

28.5

34

30

39.5

30

42

32.5

41

29

31.5

17

22.5

activity and

Ilt, or

from the relationship I v =

0.73

(H-r

to determine the plastic limit from the value of the liquid

20).

limit and the value of strength at the liquid limit. The “con­

Table III shows the actual values of plastic limit deter­ mined by standard tests and those calculated from equations

solidation pressure” causing the clay to change from a col­ loidal sediment to the liquid limit state can readily be

(1)

and (2)

and also from

curves at P

=

10 kg/sq.cm.

obtained and is not equal to zero.

CONCLUSION

The undrained shear strength of remoulded clay at a water content near to the liquid limit serves to determine the liquid limit value of the soil by means of only one test. The (e-log p) curves for various remoulded clays charac­ teristically show that most of the clays tested, as well as other clays, reach their plastic limit when consolidated at a pres­ sure near to 10 kg/sq.cm. This relationship made it possible